1. Field of the Invention
The invention relates generally to the analysis of underground earth formations, and, more particularly, to the determination of formation strength and stress properties from subsurface measurements.
2. Background Art
Detailed knowledge of geological formation stresses is desirable in the hydrocarbon production business, because formation stresses can affect the planning of well stimulation treatments to enhance hydrocarbon recovery as well as provide predictions of sanding and wellbore stability. In addition, formation stress determinations can also prove useful in determining the long-term stability of the formation and thus the suitability of the formation as a repository for waste disposal. Accordingly, there is a growing demand in the industry for the estimations or determinations of formation stresses.
There are two types of stresses important in the analysis of wellbore rock mechanics and stability: far-field stresses and wellbore stresses. Far-field stresses exist in the formation far away from the wellbore. By definition, far-field stresses are not influenced by the wellbore. Instead, they are naturally occurring in the formation. In contrast, wellbore stresses act on the formation at the mud-formation interface. The wellbore stresses are created when the wellbore is drilled. The wellbore stresses are influenced by the far-field stresses as well as the drilling fluid “mud” density.
Principal stresses refer to a coordinate system that is aligned with the stresses such that the three stresses have components normal to the reference frame. The principal stress concept simplifies the computations and explanations of the formation stresses. A Cartesian coordinate system is typically used to describe the far-field stresses. With the Cartesian coordinate system, the far-field principal stresses can be described by a vertical stress, σv, and two horizontal stresses. If the magnitudes of the two horizontal stresses are different, and they usually are, they are termed the minimum, σh, and the maximum, σH, horizontal stresses. In addition to the magnitudes of these three stresses (σv, σh, σH), the direction of either σh or σH is needed in order to the completely define the far-field stresses.
In a vertical well, a cylindrical coordinate system is typically used to describe the wellbore stresses. Here, the principal stresses include a radial stress, σr, and two orthogonal stresses: axial, σa, and tangential, σt. The radial stress (σr) is directed from the center of the wellbore out into the formation. The axial stress (σa) is directed along the axis of the borehole. The tangential stress (σt) is directed around the circumference of the wellbore. The tangential stress (σt) is also called the hoop stress because of this geometry.
FIG. 1 illustrates the principal stresses involved in well-bore rock mechanics and stability. As shown, a Cartesian coordinate system is used for the vertical and horizontal principal far-field stresses and a cylindrical reference frame for the principal wellbore stresses. For clarity, the following description assumes a vertical wellbore unless otherwise noted. However, embodiments of the invention are generally applicable and are not limited to only vertical wellbores or any particular coordinate system. For example, one of ordinary skill in the art would appreciate that embodiments of the invention may also use techniques known in the art to handle non-vertical far-field stresses and deviated wellbores.
FIG. 2 illustrates a formation stress profile. The formation stress profile depicts the variation in magnitudes of the principal stresses (i.e., far-field and wellbore stresses) as a function of the distance away from the center of a wellbore. Note that both the magnitudes and directions of the principal stresses change with the distance. Thus, the far-field vertical stress (σv) is related to the axial stress (σa) at the wellbore. This relationship is illustrated by curve 1. The far-field maximum horizontal stress (σH) is related to the tangential stress (σt) at the wellbore. This relationship is illustrated by curve 2. Similarly, the far-field minimum stress (σh) is related to the radial stress (σr) at the wellbore. This relationship is illustrated by curve 3.
Of these six stresses shown in FIG. 2, the radial stress (σr) is the only stressthat can be directly controlled by the driller. The remaining stresses are either naturally occurring (i.e., the far-field stresses) or are influenced by the far-field stresses, the engineer's choice of the radial stress (σr) (i.e., the choice of mud weights), and the physics of rock deformation (i.e., the axial stress (σa) and the tangential stress (σt)). The engineer controls the radial stress (σr) by choosing a mud density, or an equivalent circulating density (ECD). The ECD is a measure of downhole pressure converted to an equivalent mud density for the driller. ECD accounts for not only the static mud density, but also additional pressures arising from mud pump or drill string motions. In defining a radial stress profile, a formation model (rock deformation model) based on the linear elastic theory is typically used to illustrate the stress behavior. However, more complex formation models may also be used, such as non-linear elastic model, elastoplastic model, plastic model, and an explicit constitutive model.
Stresses in the earth are generally compressive and in this description, reckoned positive. The grains of the formation are forced together by compressive stresses. For example, the far-field vertical stress is caused by the weight of the overburden. Tensile stresses act in opposite directions pulling the grains apart. Different stress regimes can cause different mechanisms of yield and failure. Shear yielding, that eventually leads to shear failure, is initiated by two orthogonal stresses with sufficiently different magnitudes. Tensile yielding and failure is initiated by a single tensile stress. These two mechanisms are commonly observed in wellbore images.
When a formation is exposed to sufficiently different orthogonal stresses, the grains will be sheared apart. The shear stress, which causes shear yielding and failure, is proportional to the difference between the maximum and minimum principal stress. Conventionally, shear stress=½(maximum stress-minimum stress). As shown in FIG. 2, at about 6 or more inches away from the borehole, the maximum principal stress is slightly greater than the far-field vertical stress (σv) (e.g., curve 1) and the minimum principal stress magnitude is between the wellbore radial stress (σr) and the far-field minimum horizontal stress (σh) (e.g., curve 3). Note that the changes in the shear stress (or delta shear stress, Δss, to be explained later) (shown as curve 4) are small in regions far away from the wellbore. However, at a radial distance of about 6 inches or less, the increase in the shear stress accelerates (see curve 4). In the near wellbore region, the maximum principal stress is no longer similar in magnitude to the far-field vertical stress (σv). Instead, the tangential stress (σt) becomes the maximum principal stress. Note that as this transition occurs, the direction of the maximum stress rotates by 90 degrees, i.e., from vertical to tangential (horizontal).
Therefore, the shear stress in the region between 6 and 20 inches are proportional to ½(curve1−curve3), while the shear stress in the region from the wellbore to about 6 inches is determined by ½(curve2−curve3). The near wellbore shear stress, ½(σt−σr), is often larger than that in the far field, ½(σv−σh). This is due to the change in loading caused by the creation of the wellbore when the formation is replaced with drilling mud. The “additional loading” induced by the wellbore may be more conveniently represented by a delta shear stress (Δss) function defined as Δss=½(σ1−σ3)−½(σv−σh), where σv and σcorrespond to the vertical and minimum horizontal far-field stresses, respectively, and σ1 and σ3 correspond to the maximum and minimum stresses, respectively, at a given distance into the formation. Those skilled in the art will appreciate that the vertical stress (σv) and the minimum horizontal stress (σh) in the above equation may need to be replaced with the appropriate minimum and maximum far-field stress, respectively, for the formation being analyzed. For example, in a formation having σH>σv>σh, the maximum and minimum stresses are σH and σh, respectively. The delta shear stress function (Δss) thus defined is a more sensitive indicator of near wellbore shear stress. The shear stress or the delta shear stress (Δss) as a function of radial distance from the wellbore is referred to as a “radial stress function” in this description.
The magnitudes of delta shear stress (Δss) as a function of distance away from the borehole is illustrated as curve 4 in FIG. 2. When the drilling engineer chooses a low wellbore pressure (i.e., low ECD), the shear stress (curve 4) increases significantly near the wellbore. In the example shown, the radial stress, σr, is about one-half of the minimum far-field stress, σh. The large shear stress near wellbore may yield the formation and lead to breakouts.
As noted above, curves 1 and 2 cross over at about 6 inches from the wellbore. The cross over (mode transition) occurs at point M, where the magnitudes of the far-field vertical stress (σv) and the tangential stress (σt) are equal. This cross over point M marks an important stress mode transition because the formation behavior changes significantly at this point as a result of the 90-degree change in the direction of the maximum stress. If a logging measurement can infer a change in behavior related to this substantial increase in stress and measure the wellbore pressure that is associated with this change, significant information may be gained about the formation strengths as well as the stresses acting on the formation.
FIG. 3 illustrates the wellbore stresses as a function of the equivalent circulating density (ECD). In a vertical well, the radial stress (σr) increases with ECD; the tangential stress (σt) decreases with ECD; and the axial stress (σa) is independent of ECD. Yielding occurs when the wellbore stresses exceed the yield strength, and failure occurs when the wellbore stresses exceed the failure strength. As noted above, two mechanisms of yielding and failure (i.e., shear and tensile) are commonly observed. Shear failure occurs when the shear stress exceeds the shear strength. Shear stress, which is proportional to the difference between the maximum and minimum wellbore stress, occurs in regions marked with stipples in FIG. 3. Tensile failure occurs when a tensile stress is greater than the tensile strength of the formation. By convention, tensile stresses are negative, so any stress less than zero is tensile, as represented by the hashed areas in FIG. 3.
It is apparent from FIG. 3 that the geometry (orientation) of the failure may change with the radial stress (σr) (or ECD) because the stresses that cause the formation yielding and failure change directions. Therefore, depending on the magnitudes and orientations of the various stresses acting on a formation, several modes of formation failure are possible. For a comprehensive discussion of the various failure modes, see Tom Bratton et al., Logging-While-Drilling Images For Geomechanical, Geological and Petrophysical Interpretations, SPWLA paper JJJ, 1999.
The change in orientations of stresses acting on a formation is dependent on the far-field stresses. Thus, determination of far-field stresses is essential in the analysis of formation strength and stresses. The far-field vertical stress (σv), which depends on the overburden, can be reliably determined by integrating the formation bulk density from the surface to the depth of interest. On the other hand, the minimum (σh) and maximum (σH) horizontal stresses are conventionally derived from hydraulic fracturing tests and analyzing borehole breakouts. Specifically, observations of fracture behavior, measurements of the ECD when a vertical fracture closes, and a model of rock deformation (e.g., a linear elastic model) are typically used to invert for the minimum horizontal stress (σh). Similarly, observations of breakouts, measurements of the ECD that caused the failure, and a model of rock deformation (e.g., a linear elastic model) are typically used to invert for the maximum horizontal stress (σH). However, the accuracies of these approaches depend on the accuracies of the estimation of the formation shear strength (from formation breakouts and fractures) and the assumptions of linear elasticity.
U.S. Pat. No. 5,838,633, issued to Sinha and assigned to the present assignee, discloses methods for estimating formation in-situ stress magnitudes using a sonic borehole tool. The methods disclosed in this patent do not depend on knowledge of the formation breakouts or fractures. This patent is incorporated by reference in its entirety. The methods disclosed in this patent analyze flexural wave dispersions from dipole sources that are aligned parallel and perpendicular to the maximum far-field compressive stress direction. In addition, these methods also analyze the Stoneley wave dispersion from a monopole source. In the presence of formation and borehole stresses that are in excess of the stress levels of an isotropic reference state, the borehole flexural and Stoneley wave velocity dispersions are also functions of the formation stresses. A multi-frequency inversion of the flexural or Stoneley wave velocity dispersions over a selected frequency band may then be performed to determine the uniaxial stress magnitudes.
Similarly, U.S. Pat. No. 6,351,991 B1, issued to Sinha and assigned to the present assignee, discloses methods for determining stress parameters of formations from multi-mode velocity data, which do not depend on the formation breakouts or fractures. This patent is incorporated by reference in its entirety. The methods disclosed in this patent uses acoustic logging instruments to measure compressional velocity, fast-shear velocity, slow-shear velocity, and Stoneley velocity. Note that velocity and its inverse, the slowness, are used interchangeably in this description. These measurements together with estimates of a second set of parameters are used to derive formation in-situ stress parameters.
In addition to formation stresses, knowledge of the formation strength is also important for predicting wellbore stability and for choosing the optimal conditions to complete the wells. Formation strength is conventionally estimated from a correlation between dynamic elastic moduli or formation porosity and the unconfined compressional strength of a core sample. However, such correlation often provides rough estimates that are too inaccurate for many applications.
Improved techniques for measuring formation strength and evaluating formation stresses are desired. Further, techniques that can measure in-situ formation properties without relying on formation breakouts or fractures are needed.